{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VD26LJGS4U5JXFSUMHKKXZYYKR","short_pith_number":"pith:VD26LJGS","canonical_record":{"source":{"id":"1610.06623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T22:40:00Z","cross_cats_sorted":[],"title_canon_sha256":"b71776075c12a91d55ae2a38905b595f1379c6bed369451b7f5ad4719a42ac55","abstract_canon_sha256":"da999c289c476b14a95792177161919be66de9f38fdbbbb43e13e99a6c0e4cf2"},"schema_version":"1.0"},"canonical_sha256":"a8f5e5a4d2e53a9b965461d4abe71854657720ea73c6f4c9a6592eb512bee066","source":{"kind":"arxiv","id":"1610.06623","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06623","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06623v2","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06623","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"VD26LJGS4U5J","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VD26LJGS4U5JXFSU","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VD26LJGS","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VD26LJGS4U5JXFSUMHKKXZYYKR","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T22:40:00Z","cross_cats_sorted":[],"title_canon_sha256":"b71776075c12a91d55ae2a38905b595f1379c6bed369451b7f5ad4719a42ac55","abstract_canon_sha256":"da999c289c476b14a95792177161919be66de9f38fdbbbb43e13e99a6c0e4cf2"},"schema_version":"1.0"},"canonical_sha256":"a8f5e5a4d2e53a9b965461d4abe71854657720ea73c6f4c9a6592eb512bee066","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:59.820974Z","signature_b64":"wiotNjialiSND6mwbTDqnF4GQbi7E6BSvB4ASn5Cm5gWbiZyhghgGFYX3rhjX+e9HJbpscRIGU9Nuv+UuexSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8f5e5a4d2e53a9b965461d4abe71854657720ea73c6f4c9a6592eb512bee066","last_reissued_at":"2026-05-18T00:54:59.820300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:59.820300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06623","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NaHGwCWYxYDzKKAly29fjp5QXE1QYCrsXZIHqtpPQMBCUDzCFA6fDoPxfGbp1xACNaezAYjeaUdDY2jJuTgWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:29:23.632627Z"},"content_sha256":"909ffc9449cb2db2506c74424bd25b10980481d8674a7fd47e477800bc2d05ad","schema_version":"1.0","event_id":"sha256:909ffc9449cb2db2506c74424bd25b10980481d8674a7fd47e477800bc2d05ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VD26LJGS4U5JXFSUMHKKXZYYKR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Schrodinger-Poisson Equations With General Nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marco A. S. Souto, Ronaldo C. Duarte","submitted_at":"2016-10-20T22:40:00Z","abstract_excerpt":"In this paper we investigate the existence of positive solutions and ground state solution for a class of fractional Schr\\\"odinger-Poisson equations in $\\mathbb R^3$ with general nonlinearities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06623","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrTwOYjI7ZozetcwoOoht4Hvg80DxnivE9c3yFNNCze4OdNNv4Hknc09RkQNYO/o76ZDuv3T0ADpcdN3Fqm0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:29:23.633268Z"},"content_sha256":"5ff9b9ae90f9215d63f33014121bd74faf380ef16d9d6315f94fe9d8266123a3","schema_version":"1.0","event_id":"sha256:5ff9b9ae90f9215d63f33014121bd74faf380ef16d9d6315f94fe9d8266123a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VD26LJGS4U5JXFSUMHKKXZYYKR/bundle.json","state_url":"https://pith.science/pith/VD26LJGS4U5JXFSUMHKKXZYYKR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VD26LJGS4U5JXFSUMHKKXZYYKR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T13:29:23Z","links":{"resolver":"https://pith.science/pith/VD26LJGS4U5JXFSUMHKKXZYYKR","bundle":"https://pith.science/pith/VD26LJGS4U5JXFSUMHKKXZYYKR/bundle.json","state":"https://pith.science/pith/VD26LJGS4U5JXFSUMHKKXZYYKR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VD26LJGS4U5JXFSUMHKKXZYYKR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VD26LJGS4U5JXFSUMHKKXZYYKR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"da999c289c476b14a95792177161919be66de9f38fdbbbb43e13e99a6c0e4cf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T22:40:00Z","title_canon_sha256":"b71776075c12a91d55ae2a38905b595f1379c6bed369451b7f5ad4719a42ac55"},"schema_version":"1.0","source":{"id":"1610.06623","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06623","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06623v2","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06623","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"VD26LJGS4U5J","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VD26LJGS4U5JXFSU","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VD26LJGS","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:5ff9b9ae90f9215d63f33014121bd74faf380ef16d9d6315f94fe9d8266123a3","target":"graph","created_at":"2026-05-18T00:54:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we investigate the existence of positive solutions and ground state solution for a class of fractional Schr\\\"odinger-Poisson equations in $\\mathbb R^3$ with general nonlinearities.","authors_text":"Marco A. S. Souto, Ronaldo C. Duarte","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T22:40:00Z","title":"Fractional Schrodinger-Poisson Equations With General Nonlinearities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06623","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:909ffc9449cb2db2506c74424bd25b10980481d8674a7fd47e477800bc2d05ad","target":"record","created_at":"2026-05-18T00:54:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"da999c289c476b14a95792177161919be66de9f38fdbbbb43e13e99a6c0e4cf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T22:40:00Z","title_canon_sha256":"b71776075c12a91d55ae2a38905b595f1379c6bed369451b7f5ad4719a42ac55"},"schema_version":"1.0","source":{"id":"1610.06623","kind":"arxiv","version":2}},"canonical_sha256":"a8f5e5a4d2e53a9b965461d4abe71854657720ea73c6f4c9a6592eb512bee066","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8f5e5a4d2e53a9b965461d4abe71854657720ea73c6f4c9a6592eb512bee066","first_computed_at":"2026-05-18T00:54:59.820300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:59.820300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wiotNjialiSND6mwbTDqnF4GQbi7E6BSvB4ASn5Cm5gWbiZyhghgGFYX3rhjX+e9HJbpscRIGU9Nuv+UuexSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:59.820974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06623","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:909ffc9449cb2db2506c74424bd25b10980481d8674a7fd47e477800bc2d05ad","sha256:5ff9b9ae90f9215d63f33014121bd74faf380ef16d9d6315f94fe9d8266123a3"],"state_sha256":"9e1cfe8adb6877fa1ff9d8cdc1f051544b681aebbaa9abe24123ad4a8c5c8991"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e96fw4roHfTKoAUIFf/yDIZRZFspHcJXHf9WR0DaHSSHr0YAgE4LNXzeI/gEgC5oi+UF2TSPPf+Q7XUykkPaCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:29:23.636841Z","bundle_sha256":"d3441178d9331d52629bab6264bd9f55f01c4a68254ce1ff2ebb29c342928a54"}}